la Sauvette, dont les ingénieurs-géographes ont trouvé
![{\displaystyle {\begin{aligned}{\text{latitude}}\quad \mathrm {H} ''=&48^{\text{g}}{,}8841''{,}40\\{\text{longitude }}\mathrm {P} ''=&-4{,}4444{,}79\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8815d28e96dc759115b3f2b87c762114a7d21ff3)
(le signe
indique que les longitudes comptées à partir du méridien de Paris sont orientales.)
Il s’agit de déduire de ces seules données la plus courte distance
qui sert de base au grand triangle
or si l’on suppose que
![{\displaystyle {\begin{alignedat}{2}\log .a=&6.8046154\qquad &\log .\ \ b=&6.8032060\\\log .\varepsilon =&7.8136902&\log .e^{2}=&7.8108714,\end{alignedat}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/07900e92bc6c4892373af006b56b35d3d4998864)
on aura, par la relation (1) du § II,
![{\displaystyle {\begin{alignedat}{2}\log .{\frac {b}{a}}=&9.9985906&\log .{\frac {b}{a}}=&9.9985906\\\operatorname {l} .\operatorname {tang} .\mathrm {H} '=&{\underline {9.9820282}}&\operatorname {l} .\operatorname {tang} .\mathrm {H} ''=&{\underline {9.9738447}}\\\operatorname {l} .\operatorname {tang} .\lambda '=&9.9806188&\operatorname {l} .\operatorname {tang} .\lambda ''=&9.9724353\\\lambda '=&48^{\text{g}}{,}5799''{,}52\qquad &\lambda ''=&47^{\text{g}}{,}9810''{,}36\end{alignedat}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c443cc0f4368ad05e2445cc434c241df5c79cabf)
La relation (E’) donnera, à cause de
![{\displaystyle {\begin{alignedat}{4}\operatorname {l} .\cos .\lambda '=&9.9589595+&&&\operatorname {l} .\sin .\lambda '=&9.8395782-\\\operatorname {l} .\operatorname {tang} .\lambda ''=&{\underline {9.9724353}}&&&\operatorname {l} .\cos .\varphi =&{\underline {9.9999735}}\\&{\underline {9.8313948}}=&0{,}6782577&&&9.8395517-=-0{,}6911171\\&&&&&\qquad \qquad \qquad \ \ {\underline {+0{,}6782577}}\end{alignedat}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/70db69f0b9d5e48eb16b3ef0b933ae17a8ca7737)
![{\displaystyle {\begin{alignedat}{2}\operatorname {l} .\sin .\varphi =&8.0432820\\{\text{c. log. dénom}}.=&{\underline {1.8907793}}-&\qquad \quad {\text{dénomin}}.&=-0{,}0128594\\\operatorname {l} .\operatorname {tang} .\mathrm {Z} =&9.9340613-45^{\text{g}}{,}1855''{,}8\\&\quad \ \ {\text{ainsi }}\mathrm {Z} =154{,}8144{,}2\\\end{alignedat}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a3f32a081ef33d7f702a04538a07e8788d88a3f)
On passera de là au calcul du coefficient différentiel
et l’on aura